Specialization at T = 25/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -17748181575995562432T^8 - 68950264390727535360T^7 + 8699074436586682108080T^6 + 12741479216727376275360T^5 - 463728474595265490031140T^4 + 2963699770894322471975520T^3 - 194193238987061701313153355T^2 - 95969453985039443759130870T - 310200641841234939840019575,
A6 = 28458595086987432964730252544T^12 + 275888274364612261091053255680T^11 - 25546204540605639831811130845440T^10 - 214481134634159402629225293934080T^9 + 10021487135166118810532760404441760T^8 + 65631974027314075339317142302100224T^7 - 2153547550274428516604054291205834240T^6 - 8426270126123746622925669230499864000T^5 + 200045572563878379791949595562547381585T^4 + 160658159194208827721840972980051767780T^3 + 2225591631846316721268275361346593412191T^2 + 1041745904224145223737201675298702863910T + 2063542286683351976936829656813026126650.
It is a 2-neighbour of the fibration given in curve#4647: its Mordell-Weil lattice (rank 17, no reducible fibres) is a root-free Kneser 2-neighbour of that fibration's, realised by the pencil |O + P - F| for a section P of height 12. Constructed and searched by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.
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